Effect of the MgO/Silica Fume Ratio on the Reaction Process of the MgO–SiO2–H2O System

In order to clarify the effect of the MgO–silica fume (SF) ratio on the reaction process of the MgO–SiO2–H2O system, the reaction products and degree of reaction were characterized. Furthermore, the parameters of the reaction thermodynamics were calculated and the reaction kinetics were deduced. The results indicate that a large amount of Mg(OH)2 and small quantities of magnesium silicate hydrate (M–S–H) gels were generated upon dissolution of MgO. However, the M–S–H gels were continuously generated until the SF or Mg(OH)2 was consumed completely. For a MgO dosage less than 50% of the total MgO–SiO2–H2O system, the main product was M–S–H gel, while for a MgO dosage greater than 50%, the main product was Mg(OH)2. The results indicate that M–S–H gels have greater stability than Mg(OH)2, and the final reaction product was prone to be M–S–H gels. Based on the experimental values, an equation is proposed for the reaction kinetics of MgO.


Introduction
The MgO-SiO 2 -H 2 O system was developed as a novel cementitious material [1][2][3][4][5]. Numerous applications have been realized, including usage in thermal insulation material [6], waste sealing material [7], refractory material [8], and soil stabilization [9]. Magnesium silicate hydrate (M-S-H) gel is the typical reaction product formed in the MgO-SiO 2 -H 2 O system [7][8][9][10][11][12][13][14]. Cole [15] found a crystalline M-S-H phase, which was identified as 4MgO·SiO 2 ·8.5H 2 O. Gollop [16] found that M-S-H gel forms in Portland cement pastes by magnesium sulfate attack, and characterized the gel as a poorly crystallized serpentine (3MgO·2SiO 2 ·2H 2 O). Brew [17,18] characterized chemically synthesized M-S-H gels and investigated the incorporation of cesium and potassium. Vandeperre et al. [19] discovered that brucite (Mg(OH) 2 ) could react with the amorphous silica present in pulverized fuel ash to form M-S-H gels. In fact, the reaction products containing Mg were found to be Mg(OH) 2 and hydrotalcite-like phases, rather than M-S-H gels [20]. In addition, because magnesium is frequently associated with calcium in carbonate rocks (the raw material for cement production) [21], the existence of MgO in cement-based materials is inevitable. Overall, the reaction process of MgO in the MgO-SiO 2 -H 2 O system and the effects of the MgO/SF ratio on the reaction process are not clearly understood, and further research is necessary to clarify these reactions.
In this study, the reaction processes and reaction products of MgO/silica fume (SF) pastes were characterized. Further, thermodynamic calculations and kinetic deductions were conducted, and the Materials 2019, 12, 80 2 of 12 effects of the MgO/SF ratio on the reaction process of the MgO-SiO 2 -H 2 O system clarified. The results contribute to a better understanding of the reaction processes of the MgO-SiO 2 -H 2 O system and the development of a novel cementitious material.

Raw Materials
The chemical compositions of MgO and SF [3], as determined by X-ray fluorescence spectroscopy (XRF, PANalytical, Almelo, The Netherlands), are listed in Table 1. The particle size distributions of MgO and SF powders [3], as measured by laser diffraction (Partica LA-950V2, HORIBA, Kyoto, Japan) are presented in Figure 1. In this study, the reaction processes and reaction products of MgO/silica fume (SF) pastes were characterized. Further, thermodynamic calculations and kinetic deductions were conducted, and the effects of the MgO/SF ratio on the reaction process of the MgO-SiO2-H2O system clarified. The results contribute to a better understanding of the reaction processes of the MgO-SiO2-H2O system and the development of a novel cementitious material.

Raw Materials
The chemical compositions of MgO and SF [3], as determined by X-ray fluorescence spectroscopy (XRF, PANalytical, Almelo, The Netherlands), are listed in Table 1. The particle size distributions of MgO and SF powders [3], as measured by laser diffraction (Partica LA-950V2, HORIBA, Kyoto, Japan) are presented in Figure 1.

Preparation of MgO/SF Pastes
According to the proportions of the mixture listed in Table 2, MgO/SF pastes were prepared by mixing reactive MgO, SF, and water homogeneously, followed by sealing of the mixture in polyethylene bags and curing at room temperature (25 ± 1 °C) [3].

Preparation of MgO/SF Pastes
According to the proportions of the mixture listed in Table 2, MgO/SF pastes were prepared by mixing reactive MgO, SF, and water homogeneously, followed by sealing of the mixture in polyethylene bags and curing at room temperature (25 ± 1 • C) [3].

Preparation of M-S-H Gel
M-S-H gel with a Mg/Si ratio of 1.0 was synthesized as reported in [3]. In accordance with [17], Mg(NO 3 ) 2 ·6H 2 O solution was slowly added to a Na 2 SiO 3 ·5H 2 O solution by stirring in a flask at 0 • C. The precipitated composite was filtered and washed using ultrapure water [3].

Measurement of Heat Evolution
The heat evolution of the MgO/SF pastes [3] was measured up to day 10 at 25 • C using a TAM-Air isothermal calorimeter (Thermometric AB, Jarfalla, Sweden) according to ASTM C 1702-09 [23].

Measurement of MgO Content
The residual MgO content in MgO/SF pastes was determined by quantitative X-ray diffraction (Q-XRD, Cu Kα 1 , 40 kV and 40 mA; PANalytical B.V., Almelo, The Netherlands) using the K-value method [25], in which ZnO was used as the internal standard material.

Calculation of Mg(OH) 2 and M-S-H Gel Contents
The contents of Mg(OH) 2 and M-S-H gel were calculated according to the weight losses displayed in the DTG/TG curves, as shown in Equations (1)-(3) [3,4].

Degree of Reaction
The degree of reaction (α) of MgO was calculated using Equation (4). where C 0 (MgO) and C t (MgO) are the mass ratios of MgO in MgO/SF pastes cured at 0 and t days, respectively, which are normalized using the residual mass ratio of the samples following calcining at 1000 • C. Figure 2 shows the compressive strength and flexural strength development of MgO/SF mortar up to 90 days. The compressive strength and flexural strength increased with curing age. However, because MgO hydrated too slowly, it was not able to gain sufficient strength after day 28 and strength retrogression occurred even for M 0.8 -S 0.2 90 days later. The main reason for this is that MgO produces a large amount of Mg(OH) 2 in the later stage of the reaction. The gelling ability of Mg(OH) 2 is poor and volume expansion occurs simultaneously, which leads to a decrease in strength. The incorporation of SF with MgO resulted in higher strength because of the reaction between them, and strength increased with the increase in SF amount. M 0.5 -S 0.5 mortar has the highest strength; its compressive strength at days 3, 7, 28, and 90 is 18.4, 40.6, 64.7 and 75.6 MPa, and its flexural strength is 3.2, 5.6, 6.1 and 9.4 MPa, respectively. This phenomenon can be attributed to the fact that when the MgO content is low, the amount of M-S-H gel generated is small and the strength is low. When the MgO content is high, the reaction products are mainly Mg(OH) 2 , and the mechanical properties are poor. In general, the strength increased with curing time up to 90 days. However, it was found that further curing did not lead to any increase in strength; on the contrary, the strength sometimes decreased.

Heat Evolution
Three peaks (designated as I, II, and III, at approximately 0.5, 12, and 48 h) [5] were observed in the rate of heat evolution curves of the MgO/SF pastes (Figure 3a) [3]: the initial peak (I) is related to the exothermic wetting of the mixtures [5]; the second peak (II) corresponds to the formation of Mg(OH) 2 ; the third peak (III) is attributed to the formation of the M-S-H gel [5]. As the MgO content decreased, the second peak became less distinct, while the third peak broadened (Figure 3a), resulting in a decrease in the early cumulative heat. The cumulative heat of the M 0.4 S 0.6 paste (255.88 J/g) was lower than that of the M 0.5 S 0.5 paste (299.06 J/g) and M 0.6 S 0.4 paste (302.94 J/g) at an early curing age (100 h), while at an advanced curing age (300 h), the cumulative heats were 351.83, 370.32 and 400.05 J/g, respectively. The results indicate that the formation of Mg(OH) 2 is restrained by increasing the content of SF, which also confirms that the formation of the M-S-H gel is a continuous process [5].    [3,8]; the second endothermic valley (∆M 3 , at approximately 400 • C) occurs due to the removal of the hydroxyl from Mg(OH) 2 [4][5][6][7][8]; and, the exothermic effect at approximately 850 • C is associated with the recrystallization of the M-S-H gel [3,[12][13][14][15][16]. In addition, ∆M 2 (which is in the range 200-1000 • C) is the weight loss of the CBW from the reaction products (including Mg(OH) 2 , MgCO 3 and M-S-H gel) [3]. Here, ∆M 4 is the weight loss due to the decomposition of MgCO 3 [3,5], and the initial and final points are determined by the virtual baseline of the DSC curves (as shown in Figure 7a).  [3,8]; the second endothermic valley (∆M3, at approximately 400 °C) occurs due to the removal of the hydroxyl from Mg(OH)2 [4][5][6][7][8]; and, the exothermic effect at approximately 850 °C is associated with the recrystallization of the M-S-H gel [3,[12][13][14][15][16]. In addition, ∆M2 (which is in the range 200-1000 °C) is the weight loss of the CBW from the reaction products (including Mg(OH)2, MgCO3 and M-S-H gel) [3]. Here, ∆M4 is the weight loss due to the decomposition of MgCO3 [3,5], and the initial and final points are determined by the virtual baseline of the DSC curves (as shown in Figure 7a).

PAW and CBW Contents
Owing to the formation of M-S-H gel, the first endothermic valley gradually became prominent ( Figure 6). Therefore, the amounts of PAW and CBW associated with the M-S-H gel (shown in Figure 9) are considered to be indicative of the M-S-H gel content. The amounts of both PAW and CBW continuously increased, which is related to the gradual formation of the M-S-H gel. The amounts of PAW and CBW in the M 0.4 S 0.6 paste were higher than those in other MgO/SF pastes, which indicated that the amount of M-S-H gel in the M 0.4 S 0.6 paste is higher than that in the other MgO/SF pastes. The Mg(OH)2 content was calculated using Equation (1), the results are shown in Figure 8. The Mg(OH)2 content in the M0.2S0.8, M0.4S0.6, M0.5S0.5, M0.6S0.4, and M0.8S0.2 pastes increased to 13.29%, 22.85%, 25.27%, 35.52%, and 59.34% in the first 14 days, respectively, and then slowly decreased. No Mg(OH)2 was found in the M0.2S0.8 paste after 90 days, while a small amount of Mg(OH)2 (approximately 5%) was found in the M0.4S0.6 paste.

PAW and CBW Contents
Owing to the formation of M-S-H gel, the first endothermic valley gradually became prominent ( Figure 6). Therefore, the amounts of PAW and CBW associated with the M-S-H gel (shown in Figure 9) are considered to be indicative of the M-S-H gel content. The amounts of both PAW and CBW continuously increased, which is related to the gradual formation of the M-S-H gel. The amounts of PAW and CBW in the M0.4S0.6 paste were higher than those in other MgO/SF pastes, which indicated that the amount of M-S-H gel in the M0.4S0.6 paste is higher than that in the other MgO/SF pastes.

Reaction Thermodynamics
The laws of thermodynamics can predict the probability of a reaction, as well as the final state achieved when the reaction is completed. These laws are often used in analyzing cement-based materials [27][28][29]. Consequently, they were employed in the analysis of the reaction of the MgO-SiO2-H2O system in this study. The thermodynamic coefficients for the minerals (or species) of the MgO-SiO2-H2O system are shown in Table 3.

Reaction Thermodynamics
The laws of thermodynamics can predict the probability of a reaction, as well as the final state achieved when the reaction is completed. These laws are often used in analyzing cement-based materials [27][28][29]. Consequently, they were employed in the analysis of the reaction of the MgO-SiO 2 -H 2 O system in this study. The thermodynamic coefficients for the minerals (or species) of the MgO-SiO 2 -H 2 O system are shown in Table 3. Table 3. Thermodynamic coefficients of the minerals (or species) in the MgO-SiO 2 -H 2 O system at 25 • C, 1 bar [30]. The thermodynamic calculations (standard molar entropy ∆ r S θ , standard molar enthalpy of formation ∆ r H θ , and standard molar Gibbs free energy ∆ r G θ ) for the potential reactions of the MgO-SiO 2 -H 2 O system were computed using Equations (5)- (7):

Minerals or Species
where, ν i is the stoichiometric reaction coefficient, R = 8.314 J/(mol·K), and T is the temperature in K [3]. Here, ∆ r S θ > 0 indicates that the reaction tends to be more uniform, and ∆ r H θ < 0 indicates that it is an exothermic reaction (reactions occur spontaneously). A chemical reaction occurs spontaneously when ∆ r G θ < 0, and under an isothermal constant pressure condition [3]. Note that a higher K value signifies that the degree of reactant conversion is higher and the tendency for a positive reaction to occur is greater [3]. Some of the potential reactions of the MgO-SiO 2 -H 2 O system are listed in Table 4. Based on the ∆ f G m θ and ∆ r G θ values, M-S-H phases are more stable than Mg(OH) 2 . Furthermore, the formation of the M-S-H phases is much easier than Mg(OH) 2 , as the ∆ r G θ values of reactions 4 (−63.99 kJ·mol −1 ) and 5 (−261.32 kJ·mol −1 ) are much higher than reaction 6 (−299.58 kJ·mol −1 ). Table 4. Thermodynamic calculations for potential reactions.

Theoretical Deduction of the Reaction Kinetics Equation
The reaction process for the MgO−SiO 2 −H 2 O system was divided into two stages, as in references [3,14]. First, MgO reacted with water to form Mg(OH) 2 and then reacted with dissolved silica to form M−S−H gel [5]. Wei et al. [2,13] calculated the thermodynamics of the MgO−SiO 2 −H 2 O system and confirmed that the formation of M−S−H gel and Mg(OH) 2 occurred simultaneously. The dissolution of MgO is represented by Equation (8): The amount of MgO rapidly decreased at an early age, when the content of MgO was high, whereas the content of MgO decreased slowly when the amount of MgO was low. The reaction rate of MgO in the MgO−SiO 2 −H 2 O system is proportional to the first power of the MgO content, as shown in Equation (9): where k is the reaction rate constant. By integrating both sides, Equation (9) can be modified to Equation (10): Equation (10) can also be written as follows: The relationship between α and t is shown in Equation (12) (formulated by combining Equations (7) and (11)):

Verification of the Reaction Kinetics Equation
The estimated values of α for varying MgO/SF pastes were fitted using the above reaction kinetics equation (Equation (12)). The fitted curves and their parameters are shown in Figure 10 and Table 5, respectively. The results demonstrate that the reaction kinetics follow the well-defined kinetics equation and the correlation is obvious (R 2 > 0.97), which confirms the theoretical deduction process.  The reaction kinetics for MgO in different MgO/SF pastes were calculated using the relation between the degree of reaction (α) and curing age (t). The rate constant decreased with increasing MgO content when the dosage of MgO was lower than 50%, and increased with increasing MgO content when the dosage of MgO was higher than 50%.

Conclusions
When mixed with SF and water, MgO hydrated to form brucite, which immediately reacted with dissolved silica to produce M-S-H gel. The formation of amorphous M-S-H gel at room temperature was confirmed via XRD, TG, and microstructure analyses and the effect of the MgO/SF ratio on the reaction process of the MgO-SiO 2 -H 2 O system was discussed. XRD revealed the components of the reaction products, and TG was found to be a useful tool for determining the quantity of the reaction products. The following conclusions can be drawn from the present study: • Mg(OH) 2 results from the dissolution of MgO. M-S-H gels generates from the reaction between Mg 2+ and hydrated silica, and consequently the dissolution of Mg(OH) 2 and SiO 2 is promoted.

•
The formation reaction for the M-S-H gel is the main reaction in the MgO-SiO 2 -H 2 O system when the dosage of MgO is lower than 50%, while the formation reaction of Mg(OH) 2 is the main reaction when the dosage of MgO is higher than 50%. • Based on the thermodynamic calculations, M-S-H gels are more stable than Mg(OH) 2 . Furthermore, the formation reactions for the M-S-H gels occurred more completely than those for Mg(OH) 2 .

•
The reaction kinetics of MgO in the MgO-SiO 2 -H 2 O system conforms to α = 1 − e −kt (R 2 > 0.97). Because of the decrease in the SF dosage, the rate constant decreased with decreasing SF content when the dosage of MgO was lower than 50%. As a result of the formation rate of the M-S-H gels being lower than Mg(OH) 2 , the rate constant increased with increasing MgO content when the dosage of MgO was higher than 50%.